The goal of this paper is to apply the general formulas developed in the previous companion paper [1]} for an arbitrary smooth atomic displacement \(u_j(r)\) 
to the specific case of TBG with the relative twist angle \(\theta =1.05^\circ \) . The atomic displacement fields' configurations are computed by first fixing \(\theta \)  and then minimizing the combination of the intra-layer elastic terms and the inter-layer adhesion terms computed using generalized stacking fault energy (GSFE) functions. We do so for two sets of GSFE parameters found in the literature [2]}, [3]}. In both cases the regions of AB stacking in the moire pattern grow at the expense of the AA regions compared to just the rigid twist configuration, although the quantitative differences between the two models lead to smoother deformation fields for the set of parameters in Ref. [3]}. For both models we perform the Helmholtz decomposition of the displacement field due to the atomic relaxation (see Eq. REF ) and find that in both models it is dominated by the curl of an out-of-plane field \(\hat{z}\varepsilon ^U(x)\) . The scalar field \(\varepsilon ^U(x)\)  is in turn spatially periodic with the triangular moire pattern and it is dominated by its first Fourier harmonic (see Eqs.(REF -REF ) and Table REF ). The \(\varepsilon ^U(x)\)  field for the set of relaxation parameters in Ref. [2]} also obtains the contribution from higher Fourier harmonics, leading to larger momentum transfer in the inter-layer tunneling.
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